A BPS black hole is a background field configuration of gravity and matter that preserves some amount of supersymmetry and saturates the BPS bound. As an example, extremal black holes are sometimes BPS. Configurations of such extremal black holes exert no force on each other because of an exact balance between gravitational and gauge forces (i.e. electromagnetism). One way to see the connection is to observe that the relationship between charge and mass implied by the force balance equation looks just like the saturated BPS bound.

BPS black holes are very useful as a conceptual tool because they often permit one to check the Bekenstein formula for the black hole entropy in terms of explicit microstates. However, the statement of the 3rd law of black hole mechanics is roughly that such objects cannot form naturally.

Perhaps the most famous example of such a relationship is the near horizon geometry of black D3 branes. You can begin with the IIB supergravity background describing a stack of black branes with non-zero five form flux. The five form flux tells you the number of branes involved. The near horizon limit of this geometry looks like AdS_5 x S^5 and preserves additional supersymmetry. This is roughly how AdS/CFT was discovered.

There are lots of differences between an AdS black hole and the usual flat space black hole. The most glaring difference is that the large AdS black hole has positive heat capacity unlike the Schwarzschild black hole. What sort of properties are you interested in?